(4x-7)(5x=9)

Solution for (4x-7)(5x=9) equation:

(4x-7)(5x=9)

We move all terms to the left:

(4x-7)(5x-(9))=0

We multiply parentheses ..

(+20x^2-36x-35x+63)=0

We get rid of parentheses

20x^2-36x-35x+63=0

We add all the numbers together, and all the variables

20x^2-71x+63=0

a = 20; b = -71; c = +63;
Δ = b2-4ac
Δ = -712-4·20·63
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-1}{2*20}=\frac{70}{40}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+1}{2*20}=\frac{72}{40}
=1+4/5
$